FRASIER has entered the building – and Niles and Marty Crane couldn’t be happier. So it was when The Post corralled the stars of NBC’s late, beloved sitcom, “Frasier,” for a buoyant breakfast reunion.

The occasion? All three – Kelsey Grammer, David Hyde Pierce and John Mahoney (better known, respectively, as Frasier Crane, Seattle’s neurotic radio talk-show shrink; his meek brother, Niles, and their long-suffering father, Marty) – are appearing in major New York productions, albeit on separate stages.

And it was clear, as soon as Grammer arrived – sporting un-Frasier-like sneakers and a baggy Hawaiian-motif T-shirt – that these guys really like each other, though they live on different coasts and rarely get together, even when they’re performing blocks apart.

“We’re in rehearsals and performances, so we haven’t got time to see anyone doing anything,” Hyde Pierce complains. “By the time you get to the end of a rehearsal day, you just want to lay down and die!”

The former “Spamalot” star is currently in previews with the musical “Curtains,” which also features “Frasier” alum Edward Hibbert, who played supercilious radio restaurant critic Gil Chesterton.

Three blocks away, Mahoney is playing the mysterious Old Man in “Prelude to a Kiss,” while Grammer’s rehearsing his Henry Higgins for the New York Philharmonic’s concert version of “My Fair Lady,” running this week only, Wednesday through Saturday.

Back on Broadway, Bebe Neuwirth, a sometime member of the cast – she was Frasier’s ex, the steely Lilith Sternin Crane – is kicking up her heels in “Chicago.”

This particular morning, though, it’s a Crane clan reunion. To hear the guys tell it – over croissants, coffee and scrambled eggs, the staple of the show’s theme song – they hit it off on Day One of an 11-year run.

“What I’ll always remember is the pilot, when we actually performed for the first time in front of an audience. We knew it was a great script, and we loved each other’s work, but to hear that audience go absolutely nuts – a standing ovation at the taping of a television show! I mean, my hair stood on end!”

“Kels was a very good leader,” Hyde Pierce insists. “He set a good example for us in terms of respecting the work, but not respecting it too much – keeping a light tone.”

He and Mahoney believe some of the best episodes were the ones that Grammer also directed – like the one in which Niles is hospitalized.

“I remember at the time the critics, or at least some of the critics, were like, ‘Oh, it’s sentimental!’ñ” Hyde Pierce recalls. “But I saw it in reruns the other night and I was crying. I thought, ‘You bastards don’t know what you were talking about!’ñ”

Grammer shakes his head. “They had determined we weren’t a good show anymore,” says the star who, in 2002, pulled down $1.6 million per episode. “After five years, the critics get tired, and so they expect the rest of America to get tired of it, too. But we survived.ñ.ñ.”

“Thank God,” he murmurs, true to “Frasier” form. “I was counting the days until he went to that little kennel in the sky!”

“Kelsey’s very sentimental about the dog,” Hyde Pierce deadpans.

But they never really thought of him as a dog, they say. Eddie was more like “a temperamental actor” – one who terrorized the feral cats foolish enough to stray onto the “Frasier” lot.

“He’d try to gum them to death,” Grammer says. “He was a tough little thing. Some of the girls in the cast used to say, ‘Oh, he’s getting friendly!’ But he was never friendly. The first two years, every time they put him on John’s lap, he’d start to growl.”

Before Eddie lost his teeth, he bit Mahoney. Twice.

“I don’t blame him,” Mahoney says, genially. “I picked him up once from the back” – that was the episode in which poor Eddie got spayed – “and he whipped around and bit me. Another time, I accidentally slammed a car door on his tail.”

“An accident?” Grammer intones, in that plummy baritone. “There are no accidents.”

Somewhere along the way, they say, Eddie’s place was taken by his son, a friendly little spitfire named Enzo. But Eddie came out one last time – for the “Frasier” finale in 2004. That, they say, was a hard last hurrah.

“We were a mess all week,” Hyde Pierce confides, “and we couldn’t get through that final scene, ever. But once we were in front of the audience, we forced ourselves to hold it together, because we didn’t want to spoil it for them.”

And then someone brought in Eddie.

“That’s when I lost it,” Hyde Pierce says. “At this point, he was grizzled – completely snow white, stone deaf and potbellied. They brought him out .ñ.ñ. and it made me realize how old we’d all gotten.”

They laugh. What would it take to get them back on one stage together?

“Just try to think of things with three people in them,” Grammer offers.

“ñ’The Caretaker,’ñ” Mahoney suggests, referring to Harold Pinter’s bleak 1959 play about a racist hobo and two emotionally scarred brothers stuck in a dank London flat.

“We did a really great ‘Importance of Being Earnest’ in LA. Jane [Leeves] and Peri [Gilpin]” – Daphne and Roz, respectively, on “Frasier” – “played the two girls, Kels and I were Jack and Algernon, and of course, John played Lady Bracknell” – laughter – “because Lady Bracknell had a dog.”

“Kirk Douglas played the butler,” Grammer says, “and he was the only one who was off book. Damn him!”

But time’s getting away from them. Grammer’s got to head up to rehearse with the Philharmonic – where he promises to send everyone’s regards to Brian Dennehy, who plays the Cockney Alfred Doolittle in the “My Fair Lady” cast.